1

Unobservable shocks as carriers of contagion

Mardi Dungeya, George Milunovichb, Susan Thorpc;�

aSchool of Economics and Finance, University of Tasmania; CFAP, University of

Cambridge

bDepartment of Economics, Macquarie University

cSchool of Finance and Economics, University of Technology, Sydney

This version: 2 November 2009

Abstract

We propose an identied structural GARCH model to disentangle the dynamics of

nancial market crises. We distinguish between the hypersensitivity of a domestic market

in crisis to news from foreign non-crisis markets, and the contagion imported to a tranquil

domestic market from foreign crises. The model also enables us to connect unobserved

structural shocks with their source markets using variance decompositions and to compare

the size and dynamics of impulses during crises periods with tranquil period impulses. To

illustrate, we apply the method to data from the 1997-1998 Asian nancial crisis which

consists of a complicated set of interacting crises. We nd signicant hypersensitivity

and contagion between these markets but also show that links may strengthen or weaken.

Impulse response functions for an equally weighted equity portfolio show the increasing

dominance of Korean and Hong Kong shocks during the crises and covariance responses

demonstrate multiple layers of contagion e¤ects.

JEL classication: G01; C51

Keywords: Contagion; Structural GARCH

�Corresponding author. Tel.:+61 2 9514 7784; fax: +61 2 9415 7711.Email addresses: mardi.dungey@utas.edu.au (M.Dungey), gmilunov@efs.mq.edu.au (G. Milunovich),

susan.thorp@uts.edu.au (S. Thorp).

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1. Introduction

An important unanswered question concerning nancial crises is whether it is possible

to separately identify and measure shocks emerging from a particular source market.

As well as disrupting markets in the country where trouble begins, nancial crises may

spread turmoil into foreign markets in a phenomenon often labelled contagion.1 Here we

develop a method for separating these increased crisis-period linkages into two categories.

The rst category is hypersensitivity to information from elsewhere during a local crisis,

in other words, where turmoil at home changes the way a domestic market reacts to

news from foreign markets. The second category is changes to the impact of news from a

troubled foreign market on (potentially non-crisis) domestic markets - we restrict the label

contagionto this second e¤ect. These categories can be separately measured whenever

domestic and foreign crises are not totally coincident.2

This distinction is not an unnecessary abstraction since each category supports dif-

ferent crisis management and prevention policies. While the domestic policy makers of

a country in crisis are likely to be interested in preventing increasing hypersensitivity,

that is, preventing their own troubled market from over-reacting to external news, they

have little incentive to prevent their crisis spreading to foreign markets. On the other

hand, such a crisis may generate externalities to other countries in the form of contagion

so that governments and market participants in non-crisis countries may want to protect

their markets from foreign-sourced trouble, if possible. The existence of these externali-

ties is consistent with the agenda for coordinated global reforms in regulation, nancial

infrastructure and instrument design following major incidents.

Here we model contemporaneous linkages between nancial markets during normal

times, as well as changes during crisis periods. In order to capture the well-known clus-

tering of nancial returns, we base our analysis in a multivariate GARCH model of asset1Consistent with recent literature, we here refer to purecontagion in the terminology of Dornbusch

et al. (2000) and Kaminsky and Reinhart (2002), as distinct from crisis-driven changes in fundamentallinkages.

2Theoretical models of contagion propose mechanisms such as information asymmetry and portfoliorebalancing (Kodres and Pritsker, 2002; Yuan, 2005), institutional and regulatory linkages, and rela-tionship complexity (Allen and Gale, 2000; Brusco and Catiglionesi, 2007; Pavlova and Rigobon, 2007).Recent network theory tallies particularly well with the empirical framework developed here, see Allenand Babus, (2008).

3

market interaction. However we do not simply work with the standard spillovers from

a reduced form MGARCH, instead, we model contemporaneous structural interactions

between concurrently trading markets using an extension to the work of Caporale et al.

(2005) and Rigobon and Sack (2004) on identication via heteroskedasticity. Within the

framework we allow di¤erent regimes, corresponding to periods of tranquility and to a

series of crises experienced during the sample period. One advantage of our structural

GARCH approach is that the model identies the underlying independent shocks which

are key to sourcing transmissions between asset markets.

We also implement an innovative approach to classifying and interpreting structural

shocks by attributing them to a specic source market using variance decompositions.

Unlike previous approaches, this method is data-driven and does not rely on arbitrary

restrictions such as market hierarchies, orthogonalizations or chronology. Once we have

matched structural shocks to their market of origin, it becomes possible to track the

size and duration of innovations from any particular source and compare their relative

importance under di¤erent regimes (that is in the di¤erent crises or tranquil periods). The

rich interactions captured in our model contribute to the developing empirical literature

on cross-country and cross-asset-market crisis models. In addition, our technique can

be applied to other crises where the source of trouble is unclear, enabling observers to

distinguish the real underlying drivers of contagion from simple crisis chronology.

Data from the Asian crisis of 1997-1998 o¤ers a tangle of interrelated information

ows between regional markets; we can untangle key elements of crisis transmission using

our structural model. Taking the perspective of an international investor, we model daily

U.S. dollar returns to major equity market indices during the crises in Asia over the

period 1997-1998. The sample consists of Hong Kong, Indonesia, Korea and Thailand,

each of which had their own crises and potentially also received transmissions from other

crisis countries. The results show statistically signicant contagion between a number

of countries and some evidence for hypersensitivity. Not all signicant crisis changes

were associated with increases in market integration; several linkages weakened. Our

ndings are consistent with the hypothesis that in many cases the crisis country had

4

weak incentives to slow down the spread of turbulence to neighbors, while nearby markets

under the threat of contagion had more cause to take a proactive role in curbing the crisis

of an a¤ected neighbor, or once a crisis has developed, to look for protection either via

domestic regulation or international policy coordination.

Further analysis using innovation accounting for an equally-weighted portfolio of eq-

uity indices shows the rise in importance of Korean and Hong Kong-sourced shocks as

transmitters of contagion in the region, a reaction made more marked by the Hong Kong

markets hypersensitivity to news from Indonesia during October 1997. The cross market

e¤ects revealed by impulse responses on covariances between assets show how the covari-

ances between non crisis countries can be a¤ected by the events unfolding elsewhere.

The paper begins with a brief review of the modelling of contagion, the di¢ culties

this presents for policy makers in using the results, and how this motivates the current

paper. In Section 3 we set out the modelling strategy and Section 4 explains the dynamic

analysis. The Asian data and estimation results are reported in Sections 5 and 6. Section

7 concludes.

2. Motivation

Crisis-driven changes in the transmission of asset market shocks are often labelled

contagion. Theoretical models of contagion have emphasized the role of information ow,

(Akhigbe and Madura, 2001), portfolio rebalancing (Kodres and Pritzker, 2002) and

institutional linkages (Allen and Gale, 2000). Most recently, the linkages created through

networks in international banking have come to attention as a means of transmitting

crises through nancial institutions; for an overview see Allen and Babus (2008).

Empirical contagion models aim to measure these changes in the relationships between

asset markets. For example Rigobon (2001) emphasizes increased correlations. This may

come through increased strength of existing linkages, as in Eglo¤ et al. (2007) who inves-

tigate microstructural channels when looking at credit risk transmission, or via changes

in the parameters connecting assets, such as Yang et al. (2009). Alternatively, contagion

may be viewed as the opening of new channels of transmission during crisis, see Dungey

and Martin (2007). Other authors emphasize nonlinearities and use threshold models

5

to separate tranquil and crisis periods; such as Bae et al. (2003) and Billio and Peliz-

zon (2005) or more recently the potential for a domino e¤ect of crises in Markwat et al.

(2009). An acknowledged aspect of each of these approaches is the need to rst control

for general conditions, such as in Giesecke and Weber (2004) who control for common

e¤ects in credit default contagion, Dungey and Martin (2007) who use a common factor

approach and Eglo¤ et al. (2007) who di¤erentiate macrostructural channels.

Crisis prevention and mitigation is a key goal of nancial regulators. Suggestions for

mitigating or preventing crises include Diamond and Dybvig (1983), who argue for deposit

insurance to stop runs, and Castiglionesi (2007), who argues that central banks can use

reserve requirements to compensate for the incomplete contracts which allow contagion

to exist.3 Network theory proposes optimal degrees of connectedness between nancial

institutions, where both the number of connections and the form of those connections -

whether to the centre or periphery institutions - matters. (See Allen and Gale (2000) for

the seminal contribution but also Frexias et al. (2000), Hasman and Samartin (2008),

and for empirical evidence, Furne (2003).)

Knowing how to respond to a crisis depends on more than simply knowing that

contagion exists, or measuring the size of these e¤ects, although these are undoubtedly

important aspects. To formulate an appropriate crisis response it is also critical to be able

to trace the source of the crisis. For example, the Bank of England, viewing constraints on

the economy as emerging from the banking sector, provided nancial support to improve

banks balance sheets in order to tackle reduced credit to businesses and households.

Thus far, the empirical literature on nancial contagion has not addressed this issue, but

simply identies changes in the relationship between markets.

Here we provide a method for identifying both the existence of contagion between mar-

kets, and to identify the direction of transmission. We distinguish between contagion,

which is the impact of a crisis in one market on another non-crisis market, and hyper-

sensitivity, which is the increased sensitivity a market in crisis experiences to externally

generated shocks. The distinction between contagion and hypersensitivity is important

3Note that the Castiglionesi (2007) model has an acknowledged moral hazard problem.

6

for policy making. If a market is in crisis, it is most likely that domestic policy makers

are more concerned about hypersensitivity than contagion - that is they are concerned

about the increased reaction of the domestic economy to foreign shocks during this time,

and less concerned about the e¤ects of their own crisis on others. On the other hand,

foreign countries who are not experiencing a crisis are concerned mainly about limiting

the spread of the crisis and hence about the e¤ects of contagion. This highlights an

important tension in forming international agreements on crisis management - the incen-

tives of the crisis and non-crisis countries are quite di¤erent. In the Asian nancial crisis

of 1997-1998, for example, the actions of Malaysia in limiting capital ows from the end

of August 1998 is a good example of a country concerned with limiting hypersensitivity,

while the IMF programs of the time can be portrayed as attempts to limit contagion to

developed markets. In this paper we look to the empirical separation of these e¤ects.

3. Modelling strategy

Consider a vector of k ltered asset returns Yt;which are all potentially contempora-

neously interlinked in tranquil periods, so that the system can be described as

BYt = ut (1)

where B is a k�k matrix of coe¢ cients representing these non-crisis linkages, bij, normal-

ized on the diagonal elements of B: The lter removes non-zero means, auto-correlation,

spillovers, and contemporaneous common factors. A typical choice of lter is a VAR(1) in

returns with the US short term interest rate as an exogenous variable representing global

nancial conditions; see Forbes and Rigobon (2002). The k � 1 vector ut represents the

idiosyncratic shocks in the system,

ut = gt"t (2)

"it � iidN(0; 1) (3)

where gt is a k � k diagonal matrix. (Scaled structural innovations ut are uncorrelated.)

The underlying shocks themselves, given by k�1 vector "t; are distributed i:i:d: standard

7

normal: Appendix A gives a detailed k = 2 dimensional example of the model and

dynamics.

Here, we capture hypersensitivity and contagion as a change in the strength of linkages

between asset returns during a crisis consistent with the approach of Forbes and Rigobon

(2002), Favero and Giavazzi (2002), and Pesaran and Pick (2007) amongst others.4 (These

additional parameters can also detect nonlinearities in the mean equations associated with

the crises.) We explicitly model both the ability of countries to transmit contagion abroad

and any super-sensitivity to foreign shocks during periods of domestic crisis. In the past,

these two e¤ects have not been separately distinguished nor empirically quantied, both

being captured in a single measure. We model tranquil and crisis periods as follows:

(B+BcDt +DtBs)Yt = B�Yt = ut; (4)

with BcDt and DtBs representing the linkages present in crisis periods. Contagion

(indicated by subscript c) is modelled as the additional impact on the asset market in

home country i during a crisis in foreign country j, given by the parameters bc;ij (bc;ii = 0)

in each equation, the elements of the k � k matrix Bc. Hypersensitivity (indicated by

subscript s), is given by the parameter bs;ij in each equation (elements of the k � k

matrix Bs) measuring the additional impact of foreign shocks during a domestic crisis.

Each period of crisis is identied using an indicator variable Di;t which is one during

the crisis in home country i and zero otherwise, elements of the k � k diagonal matrix

Dt. The relevance of each instance of contagion and hypersensitivity is tested by the

signicance of the parameters bc;ij and bs;ij respectively: In the case of no contagion or

hypersensitivity in the system bc;ij = bs;ij = 0 for all i; j:

4Choice of crisis periods is described in section 5 below.

8

The detailed structure of equation (4) is

0BBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBB@

266666664

1 �b12 � � � �b1k

�b21 1 � � � �b2k...

.... . .

...

�bk1 �bk2 � � � 1

377777775+

266666664

0 �bc;12 � � � �bc;1k

�bc;21 0 � � � �bc;2k...

.... . .

...

�bc;k1 �bc;k2 � � � 0

377777775

266666664

D1;t 0 � � � 0

0 D2;t � � � 0...

.... . .

...

0 0 � � � Dk;t

377777775+

266666664

D1;t 0 � � � 0

0 D2;t � � � 0...

.... . .

...

0 0 � � � Dk;t

377777775

266666664

0 �bs;12 � � � �bs;1k

�bs;21 0 � � � �bs;2k...

.... . .

...

�bs;k1 �bs;k2 � � � 0

377777775

1CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCA

266666664

y1t

y2t...

ykt

377777775=

266666664

u1t

u2t...

ukt

377777775

(5)

and for each i

yit =kX

j=1;j 6=i

bijyjt +kX

j=1;j 6=i

bc;ijDjtyjt +kX

j=1;j 6=i

bs;ijDityjt + uit: (6)

We also model the known volatility clustering of nancial markets returns inYt: Given

the structure of (2) to (4) it is straightforward to see that

B�Yt � (0; E[Gt]); (7)

where Gt = gt"t"0tg0t is a k � k diagonal matrix of the squares of the elements of the

matrix gt.

The conditional covariance matrix of the structural shocks is a GARCH(1,1), specied

for Gt as

Gt = diag[ + � (ut�1 � ut�1)] + �Gt�1; (8)

where is a k�1 vector of constants, i, � is a k�k diagonal matrix of ARCH coe¢ cients

9

and � is a k � k diagonal matrix of GARCH coe¢ cients. So for each country i

g2ii;t = i + �iiu2i;t�1 + � iig

2ii;t�1: (9)

Since both Gt�1 and ut�1 are unobservable, we specify the system as a reduced form,

Yt= �t; where �t := (B�)�1ut = Aut: (10)

The joint conditional distribution of the vector of ltered returns is

Yt � N(0;Ht); (11)

and we work with this reduced form covariance matrix, Ht; which can be estimated as a

multivariate GARCH process in the ltered returns vector Yt, Ht = AGtA0:

Identication of the structural parameters in B� from the estimated value of Ht de-

pends on establishing the link between the structural parameters and the reduced form.

The lower diagonal elements of the reduced form covariance matrix Ht can be expressed

as 5

vech (Ht) = C0 +C1 (�t�1 � �t�1) +C2ht�1 (12)

where C0 is a k(k+1)=2� 1 vector of constant coe¢ cients, C1 is a k(k+1)=2�k matrix

of ARCH coe¢ cients , C2 is a k(k + 1)=2� k matrix of GARCH coe¢ cients and ht is a

k � 1 vector of the diagonal elements of Ht.

To establish the relationship between the coe¢ cients ofHt and the structural parame-

ters we begin with the vector of ARCH terms. Relying on the independence of structural

shocks, we set cross products to zero and write

(A �A)�1 �t�1 � �t�1 = (ut�1 � ut�1) : (13)5In the case of non-zero mean data the following expressions would be complicated by the additional

interactions of any common factors with the independent factors.

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Next we can make a similar transformation of the GARCH terms:

(A �A)�1 ht�1 = vecd (Gt�1) ; (14)

where vecd is the vector of the diagonal elements of the matrix.

If we again rewrite Ht = AGtA0 in vech (�) form and dene the required transforma-

tion of the A matrix as Av, a k(k + 1)=2 � k matrix of products of the elements of A;

then the reduced form covariance matrix is comprised of structural shocks and structural

parameters,

vech (Ht) = Av +Av� (ut�1 � ut�1) +Av�vecd (Gt�1) : (15)

Finally by substituting equation (13) and equation (14) we can link the C matrices of

the reduced-form MGARCH and the structural parameters,

vech (Ht) = Av +Av� (A �A)�1 (�t�1 � �t�1) +Av� (A �A)�1 ht�1: (16)

Estimation and identication of structural form parameters therefore depends on the

estimation of the reduced form covariance matrix expressed in terms of structural pa-

rameters. The coe¢ cients from the reduced form in equation (12) provide k(k + 1)=2

parameters in the C0 matrix, k2(k + 1)=2 parameters in each of the C1 and C2 matrices

for a total of (2k + 1)(k + 1)k=2. The structural model contains 3k(k� 1) parameters in

the B� matrix and 3k GARCH parameters for a total of 3k2: (In the four-country exam-

ple estimated below there are 48 structural parameters and 90 reduced form parameters,

unlike a conventional identication problem where the number of structural parameters

typically exceeds the number of reduced form moment conditions.)

The MGARCH structure of the model provides us with additional scores (rst order

conditions) that overcome problems of identication and endogeneity. Overcoming the

endogeneity problem of this simultaneous model is possible due to the fact that we do

not directly estimate the contemporaneous structural model but indirectly estimate struc-

11

tural parameters as part of the time-varying reduced form covariance matrix. There is no

endogeneity problem in the estimation of the reduced form covariance matrix. Structural

parameters are non-linear transformations of the reduced form parameters in this model,

and although an analytical proof of identication is di¢ cult, we have evidence for local

numerical identication since we consistently achieve convergence in the maximization

of the structural likelihood function from a range of starting values.6 Numerical iden-

tication of the structural parameters is helped by low correlation between the ltered

returns series. We also conrm the numerical identication and optimization procedure

by estimating the model from simulated data.

4. Dynamics

Innovation accounting within the SGARCH model gives a mapping of the dynamics

of transmissions between markets. We introduce a new approach to connecting each

structural shock to a source market without resorting to standard identifying restrictions

such as Choleski decomposition or long-run variance assumptions. Our method relies on

an interpretation of variance decomposition: we treat the shocks which contribute the

largest part of each domestic-market forecast error variance during the tranquil period

as emanating from that market. This interpretation is possible because we estimate the

entire (normalized) structural model and can thus work with the structural innovations

directly, rather than their reduced form counterparts. Consequently we do not need to

apply arbitrary restrictions to the structural model to trace turbulence during crises back

to a specic source.

We make tranquil period dynamics the benchmark then examine the dynamics of both

contagion and hypersensitivity e¤ects during periods of crisis. We take the position of an

international investor holding an equally weighted USD portfolio of each of the market

indices in the model, and track the impact of structural impulses on the volatility of this

naive portfolio. While this is a convenient application of the processes and e¤ects, the

6Rothenberg (1971, Theorem 7) shows that for non-linear systems of equations, under weak regularityconditions, an overly strong su¢ ciency condition for global identication of structural parameters ismet when the Jacobian matrix of partial derivatives with respect to the structural parameters has apositive determinant and the sum of the Jacobian and its transpose is positive semidenite.

12

potential for exploring contagion dynamics in this model are much wider than this simple

portfolio example. The model can be used to track individual transmission paths for

shocks from all domestic and foreign sources under each of the four crises in the sample,

separating hypersensitivity and contagion e¤ects.7

The 1�step ahead conditional forecast error variance for Yt is the tted value of the

reduced form conditional covariance matrix:

vart [Yt+1 � Et (Yt+1)] = vart [Aut+1 � Et (Aut+1)]

= Ht+1jt; (17)

treating all estimated parameter values as known with certainty.

The conditionally heteroskedastic properties of the model mean that forecast errors

vary with realized volatility at time t, and consequently each forecast error depends on the

specic history of volatility at time t and more generally on the forecast horizon (Gallant

et al. 1993 and Engle and Ng 1993). Since this process generates almost as many forecast

errors at the 1-step horizon as there are observations in the sample, we need a way of

summarizing the information without losing the value of conditioning. Here we compute

the forecast errors for both tranquil and crisis periods for each time t, and stack them by

size, creating an empirical distribution of conditional forecast error variances, e¤ectively

based on a series of random draws from the structural error distributions. We then select

empirical quantiles from the tranquil and crisis period distributions and compare the

forecast error variances and decompositions.

The forecast error variance is a non-linear function of structural parameters and

structural shocks, however the identication of structural parameters during estimation

means that it is possible to numerically identify the structural errors via the relationship

B�Yt = gt"t so that g�1t B�Yt = "t: The percentage of the forecast error variance at time

7One could ask, for example, What is the e¤ect on the volatility path of returns to the Thai stockmarket of a shock emerging from Hong Kong, during the Indonesian market crisis?, and derive animpulse response function to estimate the size and duration of this specic e¤ect.

13

t, V Di;jjt; for market return yi that is due to each structural shock "j is computed as

V Di;jjt =

�Agj;t+1jtg

0j;t+1jtA

0�ii�

Agt+1jtg0t+1jtA

0�ii

� 100; (18)

where gj;t+1jt is the jth column of the 1�period ahead forecast standard deviation matrix

gt+1jt: Each of the structural shocks "j is linked to the ith market if

V Di;jjt > VDi;mjt for m = 1; :::; k;m 6= i:8 (19)

Further, in the event that an investor holds an equally-weighted portfolio across the

k markets, the forecast error variance decomposition for the portfolio indicates the shift

in portfolio risk associated with exposure to a particular market during a crisis. The

proportion of portfolio volatility associated with each structural shock component can be

computed as

V Dp;jjt =w0Agj;t+1jtg

0j;t+1jtA

0w

w0Agt+1jtg0t+1jtA

0w� 100 (20)

where w is a k � 1 vector of portfolio weights, in our example, 1=k. Using (20) we can

compare the mean contribution of each shock to portfolio variance during the tranquil

and crisis periods.

Conditional impulse responses for the variance of the individual returns can be com-

puted using the approach of Lin (1997). For the equally-weighted portfolio the response

is the expectation at time t of the partial derivative of w0Ht+nw with respect to "2j;t ,

given by

Et

�@w0Ht+njtw

@"2j;t

�= Et

�w0A

@Gt+njt@"2j;t

A0w

�: (21)

The conditional impulse response of individual components (ij) of the portfolio co-

variance matrix is computed as

8This ordering would not be complete or unique if there were more than one market to which theshock "j contributed the majority of forecast error variance or if any two structural shocks accountedfor the same proportion of variance for one market. Neither of these cases arise in this application.

14

Et

�@Ht+njt@"2j;t

�ij

= Et

�A@Gj;t+njt@"2j;t

A0�ij

: (22)

Using the same method as for the variance decompositions, we compute an impulse

response conditioning on each time t volatility history, stack each time path into an

empirical distribution and draw out specic quantiles for comparison.

5. The Asian crisis

During 1997-1998 there were multiple crises in a number of countries in Asia across

several di¤erent classes of assets. The debate over the causes of, and links between, these

crises remains unresolved.

The discursive literature at the time of the Asian crisis viewed pressure in the Hong

Kong equity market around October 1997 as leading to pressure on equity markets in

other countries, and particularly in precipitating crisis in Korean markets. Four of the

major countries involved in the turmoil during 1997-1998 were Thailand, Indonesia, Korea

and Hong Kong. However empirical evidence on contagion during this period is mixed.

On one hand, Forbes and Rigobon (2002) nd little evidence for contagion in these

equity markets using bivariate correlation tests, and Bekiros and Georgoutsos (2008b)

reach a similar conclusion using an extreme value approach. On the other hand, each

of Baig and Goldfajn (1999), Caporale et al. (2003) and Baur and Schulze (2005) nd

statistically signicant contagion e¤ects. Markwat et al. (2009) use ordered logit models

to identify a domino e¤ect where local crisis evolve into more widespread and severe

events and Candelon et al. (2008), using multivariate synchronization indexes, nd a

sudden increase in bull and bear market synchronization among Asian stock markets in

1997. However the dynamic properties of the SGARCH model set out above allow us to

go further than testing for contagion e¤ects. We can also identify the main sources of

turbulence for each countrys crisis and gauge their relative importance to a diversied

investor.

We construct returns as the residuals from a VAR(1) on the log changes in the daily US

dollar-valued equity market indices for each country, including also the contemporaneous

15

3-month US Treasury Bill rate as a proxy for an exogenous common shock, following

Forbes and Rigobon (2002).9 The full sample runs from 2 January 1992 to 9 January

2007. Figure 1 shows the time series of returns.

The model proposed in Section 3 requires an exogenous identication of the indicator

variables, Di for i = 1; :::; k; where k is the total number of equity indices involved so we

collate crisis dates for each individual country from existing sources. We set the Hong

Kong crisis period as 27 October 1997 to 17 November 1997 (Billio and Pelizzon, 2003;

Rigobon, 2003) and the Indonesian crisis period as 1 January 1998 to 27 February 1998

encompassing the period of high volatility in returns associated with political uncertainty

and IMF negotiations. The Korean crisis occurs in the lead up to successful renegotiation

of its debt moratorium with the IMF on 24th December 1997. Clearly (Panel C in Figure

1) the volatility in this market began in late November; we designate the Korean crisis

period from 25 November 1997 to 31 December 1997. The Thai crisis in equity markets

dates from 10 June 1997 to 29 August 1997 (Billio and Pelizzon, 2003; Rigobon, 2003).

The crisis periods are shown as the narrow shaded areas in each of the panels of Figure

1.

Table 1 gives data sources and some descriptive statistics for the returns series. The

rst panel is for the entire sample, showing that ltering does not remove the non-

normality in the data and motivating the use of a structural GARCH model for the

ltered residuals to captured volatility clustering and fat tails. The following four panels

give the crisis periods chronologically, conrming that, in general, the volatility of returns

rises when a market is in crisis.

Our modelling strategy depends on the preservation of higher order dynamics in the

VAR residuals, so we tested the returns series for dependence and nonlinearity before and

after VAR ltering. Following Kyrtsou and Serletis (2006) and Bekiros and Georgoutsos

(2008a), we applied the BDS test (Brock et al. 1996) for time-based dependence (in-

dependent and identically distributed observations), the Tsay (1986) test for quadratic

9Data sources are listed in the notes to Table 1. Before estimation we removed all observations whereany market was not trading. This reduced the number of observations in the sample period from 3951to 3607.

16

serial dependence in means, the Engle (1982) LM test for nonlinearity in the variance,

and the Hinich (1982) bispectrum test for nonlinearity and Gaussianity. All tests reject

the nulls of independence and linearity before and after VAR ltering suggesting that

only linear dependence and the common shock have been removed.10 Table 2 reports sig-

nicance levels (p-values) for the Tsay, Engle and Hinich tests and Table 3 shows results

for the BDS (Brock et al. 1996).

6. Estimation results

Tables 4 to 6 gives the results of applying the model of Section 3 to the Asian dataset.

We estimate using quasi-maximum likelihood techniques (QML) via numerical methods in

Ox. Figure 2 sets out graphical evidence for model t, showing the standardized residuals

for each market and Table 2 reports p-values for tests for linear and non-linear dependence

and Gaussianity. The model accounts for much of the conditional heteroskedasticity,

skewness and kurtosis of the original ltered series seen in Figure 1, although some non-

normality remains as evidenced by the Hinich test results, and we observe a few large

outliers associated with specic market events.11 Testing failed to nd any signicant

ARCH e¤ects in any of the standardized residuals series. The Tsay and Hinich tests

for linearity in means are not rejected at the 5% level for Hong Kong, Indonesia and

Thailand standardized residuals but the results are somewhat weaker for Korea. Table

3 shows p-values for the BDS test which fail to reject pure randomness for all but the

Indonesian residuals. We view these results with caution given the problems with test size

and interpretation that can arise when applying this test to the residuals of a non-linear

model. (See Brooks and Heravi 1999, and Brooks and Henry 2000.)

10We also tted a multivariate Mackey-Glass model (Kyrtsou and Labys 2006) as an alternative to theVAR(1) but found no substantial di¤erence to the ltered residuals and so selected the simpler VAR(1)model. Results for the Mackey-Glass lter are available from the authors on request.11The large outlier in March 1996 in the Hong Kong series shows the signicant falls in this market

and through the region due to concerns over China. A number of events appear to be linked with theoutliers for the Indonesian returns, including the opening of the market to full foreign ownership inOctober 1993, general regional volatility in April 1998, the Bali bombings in October 2002 and politicaluncertainty combined with major earthquakes in May 2006. The September 11 attacks show up in theoutlier in the Korean series and a panic over currency regulations in December 2006 creates an outlierin the Thai series. Model estimation is robust to the removal of these large outliers. We do not reportresults separately here but they are available from the authors on request.

17

Table 4 shows the tranquil period coe¢ cient estimates. There are signicant linkages

between a number of the equity markets. The reported coe¢ cients show the impact of

returns from the markets in the table row on the corresponding column market return.

Reading down each column, the returns to the Hong Kong index exhibit a signicant

positive relationship with returns in Indonesia, (0:086) and Korea (0:296): Indonesian

returns are also signicantly a¤ected by Hong Kong (0:103) while the Korean returns are

positively related to Indonesias (0:148) but negatively related to Hong Kongs (�0:125)

during periods of tranquility. The Thai market appears to import a positive impact from

all three neighbors in the tranquil period, but does not inuence the other markets (as

evident in the last row of Table 4).

Hypersensitivity occurs when the connections between domestic markets and foreign

markets change during a domestic crisis period (Table 5). The coe¢ cients in this table

represent the impact due to crises in markets in the column headings but felt via the

returns from (non-crisis) markets in the rows, hence hypersensitivity. Only one linkage

is statistically signicant and positive in Table 5. This represents positive hypersensitivity

of the Hong Kong market to Indonesian returns (0:814) during the Hong Kong crisis.

Two more linkages are signicant and negative. Korean returns covaried negatively with

Indonesian returns during the Korean crisis (�0:753) and that Hong Kong returns varied

negatively with Korean returns during the Hong Kong crisis, (�0:751).

The negative coe¢ cients represent an interesting addition to the literature, in that

they suggest that during periods of crisis, links between two markets may move in either

direction. This is consistent with Forbes and Rigobon (2002) who nd a fall in conditional

correlation in many instances, and with the network literature where reduced linkages

during crises are also consistent with lower correlation.

Contagion occurs when a local market is a¤ected by crisis in other countries. Table 6

shows the strength of these e¤ects. In this table contagion e¤ects arise from crises in the

row markets and impact on returns to the (non-crisis) column market. Results show that

Indonesia experienced contagion from Korea during the Korean crises (0:727). During the

Hong Kong crisis (rst row of the table), Korea experienced signicant positive contagion

18

e¤ects from Hong Kong (0:665) while Thailand was impacted negatively by Hong Kong

returns (�0:504):

Table 7 provides the parameter estimates for the GARCH behavior of the underlying

shocks. In each of the cases there is a small positive and signicant constant and signif-

icant ARCH and GARCH e¤ects. The combined ARCH and GARCH parameters sum

close to one in each case.

A likelihood ratio test of the hypothesis that all hypersensitivity and contagion dum-

mies are zero yields a test statistic of 78:24 � �224 which has a p-value close to zero.

In summary we nd evidence for shifts in the relationships between the equity mar-

kets of Hong Kong, Indonesia, Korea and Thailand during the crisis period, but these

e¤ects are not uniform in direction or signicance across countries and crises. In terms

of strengthening e¤ects, the Hong Kong crisis had a large impact on regional markets,

generating signicant contagion in Korea but creating a weakening link with Thailand,

where correlation fell (Table 6). During the Hong Kong crisis in October 1997, the Hong

Kong market also became less sensitive to news from Korea but more sensitive to news

from Indonesia (Table 5). Combining the results reported in Tables 5 and 6, it is appar-

ent that the Korean crisis later that year transmitted additional turbulence to Indonesia,

but at the same time returns from Indonesia became signicantly less inuential for the

Korean market, possibly suggesting that the domestic turmoil both created trouble for

the neighboring market and drowned out feedback from outside. We observe this same

e¤ect in relation to Hong Kong and Korea. During the Hong Kong crisis Korea receives

signicant positive contagion (0:665) but Korean returns are dampened into Hong Kong

(�1:981 in Table 5). By way of contrast, the signs on the contagion and hypersensitiv-

ity parameters connecting Hong Kong and Indonesia indicate an amplication in both

directions: the Hong Kong crisis had signicant positive contagion e¤ects on Indonesia

(0:103 in Table 6) but returns in Indonesia also had a signicant positive hypersensitivity

e¤ect on Hong Kong during the Hong Kong crisis (0:814 in Table 5). The linkages be-

tween markets clearly take a number of forms and their interaction displays a complexity

previously not disentangled.

19

6.1. Variance decomposition

The rst panel of Table 8 gives the tranquil period decomposition at one step ahead,

with 5th and 95th quantile measures.12 We use these results to allocate the shocks to their

source market. In each case, we label the shock that makes the greatest contribution to

volatility in each of the tranquil-period decompositions as the own-country shock.13 The

columns in the table refer to the volatility in each asset (or portfolio), and the rows to the

contributing sources of shock. Own-country shocks contribute at least 80% of forecast

error variance in each case. The maximum impact from another country at the mean is

17% (the link from Korean shocks to the Hong Kong market). The nal column in Table

8 gives the variance decompositions for the equally weighted portfolio which also account

for covariance between the returns. In the tranquil period, Korean and Indonesian shocks

are dominant, at 39% and 31% of the total whereas Hong Kong and Thailand contribute

around 15% each.

The second panel of Table 8 shows the variance decompositions relating to links due to

hypersensitivity during crisis periods.14 There are substantial changes from the tranquil

period. The contribution of domestic shocks is diminished and the impact of Indonesia

increases commensurately. For Hong Kong, Indonesian shocks dominate the local e¤ect,

contributing half the forecast error variance. For the equally-weighted portfolio, results

show an increased contribution of 30 percentage points from Indonesia (60%) and about

5 percentage points more from Hong Kong. The contribution from Korea is reduced,

most likely due to the changing link between Indonesia and Korea.

During an external crisis, contagion links also create dramatic changes. The third

panel of Table 8 shows that the contribution of domestic market shocks to the one-step-

ahead variance decomposition is reduced under foreign crises compared with the tranquil

period for three of the four markets. Change is most dramatic for Indonesia where the

contribution from domestic shocks drops by 57 percentage points to a mean contribution

12The variance decomposition is constructed for all t possible conditionings in the sample. A histogramof these outcomes gives the mean and quantiles reported in Table 8.13The results at 5 steps ahead conrm our classication.14All insignicant parameters are set to zero when variance decompositions and impulse response

functions are computed.

20

of 42%; contagion from Korea (46%) and Hong Kong (12%) account for this. The contri-

bution of the domestic shock for Hong Kong falls by about 10 percentage points to 71%

in favour of an increase in Korean contribution to 26%. The contribution of domestic

shocks for Korea decreases by about 17 percentage points, and the inuence of Hong

Kong rises from less than 1% to 15%. There is no real change in the Thai decomposition.

Hence, Hong Kong and Korean shocks are clearly important in all countries apart from

Thailand. This is also evident in the portfolio results, where the contribution of Hong

Kong increases by 7 percentage points to 22% and the Korean contribution increases to

57% due to contagion e¤ects. However, there are falls in the percentage contributions of

Indonesia and Thailand to portfolio variance.

6.2. Impulse response functions

Figure 3 presents impulse responses in the variance of the equally weighted portfolio

to unit (one standard deviation) shocks from Hong Kong, Indonesia, Korea and Thailand

respectively. The left column shows the impulse response in the tranquil period, and

the right column shows the responses with contagion e¤ects. Using the unconditional

(sample) portfolio variance as a basis for calculation, a 0.1 increase in portfolio variance

on the vertical axis is approximately equal to a 0.6 percentage point (60 basis point)

increase in annualized portfolio volatility.

A structural shock associated with Hong Kong (Panel A) in the tranquil period is

the smallest of those investigated here, and takes about two months to dissipate half the

initial impact. When we account for contagion, however, the e¤ect of a one standard

deviation shock is to raise variance by a factor of ve over the tranquil period, with

increases persisting above the initial tranquil period impact for well over three months.

Patterns for impulses to structural shocks from Indonesia (Panel B) are remarkably

di¤erent. The initial impact of a one standard deviation shock in the tranquil period

is much larger and the distribution of responses is also more dispersed. By contrast,

contagion e¤ects are small in this case, so that unlike Hong Kong, impulse responses for

shocks from Indonesia in tranquil and contagion periods are alike though the dispersion

is greater during the contagion period.

21

The impact of Korean shocks (Panel C) in the tranquil period is greater than for Hong

Kong, but not so large as for the Indonesian case already discussed. During the tranquil

period there are statistically signicant linkages with all the other countries in the sample,

as shown in Table 4. The contagion e¤ects are substantial, with the size of the initial

shock in the external crisis scenario being ve-fold the tranquil period shock. Half of this

impact has dissipated by 45 days after the shock, but some e¤ect is still present nearly

a year after the initial shock. As a result of the lack of linkages from Thailand to other

markets, the impulse responses to shocks originating from Thailand (Panel D) are small

and do not change between the tranquil and contagion periods.

Overall, the largest contributors to volatility are the Hong Kong and Korean crises.

Shocks from these events increase portfolio variance by between around ve times and

persist for a number of months.

Another way to view contagion is via impulse responses on specic covariances. Im-

pulse responses of the equally-weighted portfolio variance average over the whole co-

variance matrix and can inform diversied investors, whereas responses of individual

covariances detail bivariate market links rather than averaging across them, measuring

contagion directly. This technique can also give a breakdown of the way interrelationships

changes during a crisis.

Figure 4 shows impulse responses of four of the six covariances to a one standard devi-

ation shock from the Hong Kong market. The array of di¤erent reactions is illuminating.

Panel A shows the impulse response for the Hong Kong-Indonesia covariance. We see

that the tranquil market link between the Hong Kong and Indonesian markets is weak,

and a shock has a very small impact, whereas the additional contagion period channel

raises covariance responsiveness by a factor of 10 and takes around two months for half

the e¤ect to dissipate. In Panel B, the impulse to the Hong Kong-Korea covariance is ac-

tually negative under normal market conditions, but crisis contagion shifts the covariance

to a strong and persistent positive. By contrast, Panel C sets out the impulse response

to the covariance between Hong Kong and Thailand. Whereas the correlation between

these markets is normally positive and Hong Kong shocks tended to raise the conditional

22

covariance, during the crisis the links between Thailand and the rest of the region weak-

ened, and the response of the covariance shifts from positive to negative. Finally, Panel

D shows an example of crisis-driven changes at a secondary level. The Hong Kong shock

is irrelevant to the Indonesia-Korea covariance in tranquil markets but contagion creates

additional transmissions amongst the markets, increasing the covariance from zero to

0.12, even though neither of these markets is the source of the news. The remaining co-

variances (Indonesia-Thailand and Korea-Thailand) were very marginally a¤ected by the

Hong Kong shock, both responding slightly more negatively when a¤ected by contagion.

The impulses of the covariances reveal some of the complexity of the linkages which

occur during crises. Assessing the e¤ects of shocks originating in one country is com-

plicated by both the crisis market transmissions to other markets via contagion and the

potential for changes in the reaction of the crisis market to information from other mar-

kets via hypersensitivity. However, there are also discernible secondary level e¤ects so

that non crisis countries experience increased covariances with each other even though

the e¤ects are not a direct impact of the news from the crisis country. These e¤ects are

realizations of the interrelatedness of the system.

7. Conclusion

We develop a model which contributes a renement to the taxonomy of crises: we

distinguish between hypersensitivity and contagion. A market which is in crisis may

transmit that crisis towards other markets, denoted contagion, and it may simulta-

neously become more or less sensitive to the e¤ects of shocks from non-crisis markets,

denoted hypersensitivity. This distinction has some importance in policy discussions.

A country experiencing a crisis is likely to be concerned primarily with preventing the

impact of hypersensitivity while countries which are not themselves in crisis are more

concerned to prevent the spread of the crisis via contagion e¤ects. Policy design for crisis

prevention and management need to be incentive compatible with the actively operating

links. This suggests that authorities require a substantial degree of discretion to actively

manage crises, as their characteristics vary greatly in terms of the directions and strength

of changes in linkages from tranquil to crisis periods.

23

In particular, our results suggest that during the Asian crisis, the crisis countries

themselves had at best weak incentives to slow the spread of turbulence, while the nearby

markets had reason to look for protection either via domestic regulation or through

international policy coordination.

The modelling framework separates hypersensitivity and contagion based on a mul-

tivariate GARCH framework with regimes and exogenously dened crisis periods. An

advantage is that structural parameters can be identied from the reduced form. Unlike

past work, which has relied on arbitrary restrictions to classify the sources of unobserv-

able structural shocks, we use variance decompositions to label the structural shocks and

connect them to source markets. This approach enables an economic interpretation of

risk transmission in tranquil and crisis periods.

Applying this model to four Asian equity markets during the East Asian crisis period

of 1997-1998, we observe statistically signicant contagion links and hypersensitivity. Im-

portantly, these changes are not always positive. The Thai market, for example becomes

more detached from shocks from near neighbors during their crises. Hong Kong trans-

mitted its crisis via contagion e¤ects to both Korea and Thailand, while at the same time

becoming more sensitive to news from Indonesia and less sensitive to news from Korea.

Similarly, during the Korean crisis, Korea transmitted its crisis via contagion to Indonesia

but simultaneously became less sensitive to Indonesian market news. From an investment

perspective, decomposing the portfolio volatility of an equally-weighted portfolio of the

four equity assets identies the redistribution of sources of turbulence away from home

market and towards outside. Impulse response analysis shows the increasing dominance

of Korean and Hong Kong shocks during the crisis, while variance decompositions conrm

this e¤ect and also highlight heightened sensitivity to Indonesian sourced shocks during

crises in other countries. An examination of the cross market linkages revealed the variety

of e¤ects operating during the crisis period.

This new framework and application contribute a breakdown of the directional ef-

fects of the relationship between asset markets during crisis. The model has a number

of similarities with the recent theoretical network literature on linkages between nancial

24

institutions, where those institutions care about inow from, and outow to, counter-

parties; see Allen and Babus (2008) for an overview. Future work linking the empirical

framework developed in this paper and network theory should provide insights into the

credit crunch of 2007-2008.

Acknowledgments

We thank Andrea Cipollini, John Geweke, Tony Hall, Gordon Menzies, Adrian Pa-

gan, Peter Phillips, Remco Zwinkels and participants at the 2007 INFINITI Conference,

Trinity College Dublin, the 2008 NCER Frontiers in Financial Econometrics Workshop,

Queensland University of Technology Brisbane, and an anonymous referee for helpful com-

ments. Part of this paper was written while Thorp was a Visiting Scholar at Cambridge

Endowment for Research in Finance, University of Cambridge. Thorp acknowledges the

support of ARC DP0877219.

Appendix A. Two-asset illustration

Here we present a two-dimensional illustration of the main features of the model and

dynamics.

The tranquil period model for VAR-ltered returns for asset markets 1 and 2, denoted

by y1t and y2t; is:

y1t = b12y2t + g11;t"1t (A.1)

y2t = b21y1t + g22;t"2t; (A.2)

which can be extended for crisis periods to

y1t = b12y2t + bs;12D1ty2t + bc;12D2ty2t + g11;t"1t (A.3)

y2t = b21y1t + bs;21D2ty1t + bc;21D1ty1t + g22;t"2t; (A.4)

where the binary dummy variables, D1t and D2t take the value 1 during periods of crisis

experienced in y1t and y2t respectively, and 0 otherwise. Data in the crisis periods provide

25

the extra information needed to identify the contagion parameters. For the rest of the ex-

ample, we work with the simpler tranquil period model. The matrix of contemporaneous

market linkages is normalized on the diagonal to give,

B =

264 1 �b12�b21 1

375 (A.5)and

B�1 : = A =

264 a11 a12a21 a22

375 : (A.6)The GARCH processes on "i in this case are:264 g211t 0

0 g222t

375 = diag8>:264 1 2

375+264 �11 00 �22

375264 u21t�1u22t�1

3759>=>;

+

264 �11 00 �22

375264 g211t�1 0

0 g222t�1

375 : (A.7)so that gii;t"it = uit:

To estimate the simple model structure in (A.1) and (A.2) we need to account for the

covariance between yit and ujt and the identication of structural parameters, and we

resolve both estimation issues by working with the reduced-form covariance matrix.

For two assets, the reduced form covariance matrix vechHt = Avvecd (Gt) from

equation (12) can be expressed as

266664H11;t

H21;t

H22t

377775 =266664

a211 a212

a11a21 a12a22

a221 a222

377775�8>:264 1 2

375+264 �11u21t�1�22u

22t�1

375+264 �11g211t�1�22g

222t�1

3759>=>; (A.8)

26

From (13) above we can write

�t�1 � �t�1 = Aut�1 �Aut�1

=

264 (a11u1t�1 + a12u2t�1)2(a21u1t�1 + a22u2t�1)

2

375264 �21t�1�22t�1

375 =264 a211 a212a221 a

222

375264 u21t�1u22t�1

375264 a211 a212a221 a

222

375�1 264 �21t�1

�22t�1

375 =264 u21t�1u22t�1

375 (A.9)using the assumption that the structural shocks are independent so that cross products

in u1t and u2t can be set to zero. From equation (14)

ht�1 =

264 H11t�1H22t�1

375 =264 a211 a212a221 a

222

375264 g211t�1g222t�1

375264 a211 a212a221 a

222

375�1 264 H11t�1

H22t�1

375 =264 g211t�1g222t�1

375 (A.10)If we rewrite Ht in vech (�) form and dene the requisite transformation of the A matrix

as Av then

266664H11;t

H21;t

H22t

377775 =266664

a211 a212

a11a21 a12a22

a221 a222

377775

8>>>>>>>>>>>>>>>:

264 1 2

375+264 �11 00 �22

375264 a211 a212a221 a

222

375�1 264 �21t�1

�22t�1

375+

264 �11 00 �22

375264 a211 a212a221 a

222

375�1 264 H11t�1

H22t�1

375

9>>>>>>>>=>>>>>>>>;(A.11)

A.1. Dynamics

The proportion of the forecast error variance for return to domestic market one, y1;

27

that is due to structural shock "1 is

V D1;1jt =a211g

21;t+1jt

a211g21;t+1jt + a

212g

22;t+1jt

(A.12)

and due to structural shock "2 is

V D1;2jt =a212g

22;t+1jt

a211g21;t+1jt + a

212g

22;t+1jt

(A.13)

The proportion of portfolio error variance for an equally weighted portfolio includes the

impact of diversication, and error sourced in "1 would be represented by the following

expression,

V Dp;1 =�g21;t+1jt

�a211 + 2a21a11 + a

221

��=�

g21;t+1jt�a211 + 2a21a11 + a

221

�+ g22;t+1jt

�a212 + 2a12a22 + a

222

��: (A.14)

Impulse responses in this case are

Et

�@w0Ht+1w

@"21;t

�= Et

8>:@264(1=2)2 [g21;t+1jt (a211 + 2a21a11 + a221)

+g22;t+1jt (a212 + 2a12a22 + a

222)]

375 =@"21;t9>=>;

= (1=2)2�a211 + 2a21a11 + a

221

�Et

(@g21;t+1jt@"21;t

)(A.15)

which creates a recursion in the structural parameters so that for an initial shockEt�"21;t�=q

Et�"21;t�= 1 in period t;

g21;t+1jt = 1 + �1u21;t + �1g

21;t (A.16)

Et

(@g21;t+1jt@"21;t

)= �1g

21;t (A.17)

and

Et

�@w0Ht+1w

@"21;t

�= (1=2)2

�a211 + 2a21a11 + a

221

��1g

21;t: (A.18)

28

For the covariance conditional impulse response functions we compute

Et

�@Ht+1@"21;t

�ij

= a21a11�1g21;t: (A.19)

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Tsay, R. S., 1986. Nonlinearity tests for time series. Biometrika 73, 461-466.

Yang, J., Zhou, Y., Wang, Z., 2009. The stock-bond correlation and macroeconomicconditions: One and a half centuries of evidence. Journal of Banking and Finance, 33,670-680.

Yuan, K., 2005. Asymmetric price movements and borrowing constraints: A rationalexpectations equilibrium model of crises, contagion, and confusion. Journal of Finance60, 379-411.

31

Figure 1: Time Series of Filtered Daily Returns to Asian Equity Price Indices,

January 1992 to January 2007.

-20

-10

0

10

20

A. Hong Kong returns

-40

-30

-20

-10

0

10

20

30

B. Indonesia returns

-20

-10

0

10

20

C. Korea returns

-16

-12

-8

-4

0

4

8

12

16

D. Thailand returns

1992 1994 1996 1998 2000 2002 2004 2006

1992 1994 1996 1998 2000 2002 2004 2006

1992 1994 1996 1998 2000 2002 2004 2006

1992 1994 1996 1998 2000 2002 2004 2006

Note: Each series is the residuals from a VAR(1). Grey bars indicate the period designated

as crisis period in each country. Data sources are described in Table 1.

32

Figure 2: Standardized residuals from tted SGARCH model,

January 1992 to January 2007.

-8

-4

0

4

8

A. Hong Kong standardized residual

-12

-8

-4

0

4

8

B. Indonesia standardized residual

-10.0

-7.5

-5.0

-2.5

0.0

2.5

5.0

C. Korea standardized residual

-12

-8

-4

0

4

8

D. Thailand standardized residual

1992 1994 1996 1998 2000 2002 2004 2006 1992 1994 1996 1998 2000 2002 2004 2006

1992 1994 1996 1998 2000 2002 2004 2006 1992 1994 1996 1998 2000 2002 2004 2006

Note: Each series is the structural residual from the tted SGARCH model standardized

by the tted conditional structural standard deviation for the relevant market and time period

33

Figure 3: Impulse Response Functions of Equally Weighted Portfolio Variance toa Standard Deviation Shock for Periods of Tranquility and Contagion

Tranquil Period ContagionA. Hong Kong sourced shock

0.0

0.1

0.2

0.3

1 33 65 97 129 161 193 225

days

0.0

0.1

0.2

0.3

1 33 65 97 129 161 193 225

days

B. Indonesian sourced shock

0.0

0.2

0.4

0.6

0.8

1.0

1 33 65 97 129 161 193 225

days

0.0

0.2

0.4

0.6

0.8

1.0

1 33 65 97 129 161 193 225

days

C. Korean sourced shock

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1 33 65 97 129 161 193 225

days

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1 33 65 97 129 161 193 225

days

D. Thai sourced shock

0.00

0.02

0.04

0.06

0.08

0.10

0.12

1 33 65 97 129 161 193 225

days

0.00

0.02

0.04

0.060.08

0.10

0.12

1 33 65 97 129 161 193 225

days

Note: Vertical axes show the absolute increase in the daily variance of an equally-weightedportfolio of the equity indices n-days after a one standard deviation structural shock from eachequity market. Impulse response functions are calculated conditioning on volatility at everytime = t in the sample. The dashed lines represent the 5th and 95th quantiles of the empiricaldistribution of the conditional impulse responses and the solid line represents the median.

34

Figure 4: Impulse Response Functions of Market Covariances toa Standard Deviation Shock from Hong Kong for Periods of Tranquility and Contagion

Tranquil Period ContagionA. Hong Kong-Indonesia

0.0

0.1

0.2

0.3

1 33 65 97 129 161 193 225

days

0.0

0.1

0.2

0.3

0.4

0.5

0.6

1 33 65 97 129 161 193 225

days

B. Hong Kong-Korea

-0.10.00.10.20.30.40.50.6

1 33 65 97 129 161 193 225

days

-0.10.00.10.20.30.40.50.6

1 33 65 97 129 161 193 225

days

C. Hong Kong-Thailand

-0.1

0.0

0.1

0.2

0.3

1 33 65 97 129 161 193 225

days

-0.1

0.0

0.1

0.2

0.3

1 33 65 97 129 161 193 225

days

D. Indonesia-Korea

-0.1

0.0

0.1

0.2

0.3

1 33 65 97 129 161 193 225

days

0.0

0.1

0.2

0.3

0.4

1 33 65 97 129 161 193 225

days

Note: Vertical axes show the absolute increase in the daily covariance between selected equityindices n-days after a one standard deviation structural shock from Hong Kong equity market.Impulse response functions are calculated conditioning on volatility at every time = t in thesample. The dashed lines represent the 5th and 95th quantiles of the empirical distribution of

the conditional impulse responses and the solid line represents the median.

35

Table 1:Descriptive Statistics for Equity Returns: Tranquil Period and Crisis Periods

Hong Kong Indonesia Korea Thailand(HK) (IN) (KO) (TH)

Total Period: 2 January 1992-9 January 2007Mean 0.000 0.000 0.000 0.000Std dev. 1.606 2.456 2.169 1.885Skew 0.016 -1.436 -0.127 0.168Kurt 13.354 40.469 12.977 9.500J-B p-val 0.000 0.000 0.000 0.000

Thai crisis: 10 June 1997 - 29 August 1997Mean -0.061 -0.642 -0.053 -0.500Std dev. 1.662 2.487 1.062 3.832Skew -0.390 -0.857 -0.102 0.079Kurt 4.942 4.128 2.751 3.190J-B p-val 0.001 0.007 0.884 0.930

Hong Kong crisis: 27 October 1997 - 17 November 1997Mean -0.353 -0.168 -0936 -0.450Std dev. 6.767 5.155 4.936 3.776Skew 0.700 1.010 0.210 0.271Kurt 5.046 3.631 2.325 2.204J-B p-val 0.129 0.226 0.810 0.734

Korean crisis: 25 November 1997 - 31 December 1997Mean 0.137 -0.723 -1.191 -1.002Std dev. 2.435 7.671 10.916 2.942Skew -0.485 -0.331 0.333 0.288Kurt 2.959 5.737 2.010 2.969J-B p-val 0.612 0.016 0.477 0.841

Indonesian crisis: 5 January 1998 to 27 February 1998Mean -0.019 -1.599 0.496 1.166Std dev. 3.982 11.600 5.193 5.310Skew 0.496 -0.527 -0.461 -0.034Kurt 4.360 4.538 2.976 3.4168J-B p-val 0.112 0.069 0.520 0.872

Note: Returns are computed as percentage log changes in the price indices for Hong Kong(Hang Seng HNGKNGI), Indonesia (Jakarta Composite JAKCOMP), Korea (Korea

Composite KORCOMP) and Thailand (Bangkok SET BNGKSET) using daily series fromDatastream, translated to US dollars before returns are computed. Sample runs from 2

January 1992 to 9 January 2007 but observations where there is a zero return from any seriesare removed before de-meaning, leaving 3607 days. Returns are ltered using a VAR(1) in thereturns and the contemporaneous daily 3-month US Treasury Bill secondary market mid-rate

(FRTBS3M).

36

Table 2:Tests for linearity and Gaussianity in returns, VAR residuals and standardized

SGARCH residuals.

p� valuesTsay (1986) Engle (1982) Hinich (1982)8 lags 8 lags 210 lattice points

H0 Linarity in mean no ARCH Linearity GaussianityReturns, ritHong Kong 0.000 0.000 0.000 0.000Indonesia 0.000 0.000 0.000 0.000Korea 0.000 0.000 0.000 0.000Thailand 0.000 0.000 0.000 0.000

VAR residuals, yitHong Kong 0.000 0.000 0.000 0.000Indonesia 0.000 0.000 0.000 0.000Korea 0.000 0.000 0.000 0.000Thailand 0.000 0.000 0.000 0.000

Standardized residuals, "itHong Kong 0.544 0.789 0.279 0.002Indonesia 0.050 0.150 0.939 0.006Korea 0.020 0.780 0.005 0.000Thailand 0.654 0.086 0.093 0.000

Note: Table reports p-values for Tsay (1986) test for linearity in means, Engle (1982) test forARCH e¤ects, and Hinich (1982) bispectrum test for linearity and Gaussianity, for returns

(log changes in US dollar values of equity price indexes), residuals from VAR(1) ltering of thereturns series including contemporaneous values of the 3 month US T-bill, and the

standardized structural residuals from the SGARCH model tted to the VAR residuals. Forcomputation of test statistics see Kyrtsou and Serletis (2006).

37

Table 3:BDS tests for departures from randomness in returns, VAR residuals and standardized

SGARCH residuals.

p� valuesReturns, rit VAR residuals, yit Standardized residuals, "it

distance; " 0:5� � 1:5� 2� 0:5� � 1:5� 2� 0:5� � 1:5� 2�Hong Kongm = 2 0 0 0 0 0 0 0 0 0.583 0.607 0.909 0.494m = 3 0 0 0 0 0 0 0 0 0.611 0.734 0.958 0.513m = 4 0 0 0 0 0 0 0 0 0.394 0.495 0.721 0.673m = 5 0 0 0 0 0 0 0 0 0.266 0.292 0.398 0.959m = 6 0 0 0 0 0 0 0 0 0.105 0.144 0.212 0.652Indonesiam = 2 0 0 0 0 0 0 0 0 0 0 0.0002 0.006m = 3 0 0 0 0 0 0 0 0 0 0 0 0.002m = 4 0 0 0 0 0 0 0 0 0 0 0.0004 0.005m = 5 0 0 0 0 0 0 0 0 0.001 0.001 0.004 0.025m = 6 0 0 0 0 0 0 0 0 0.003 0.003 0.013 0.050Koream = 2 0 0 0 0 0 0 0 0 0.101 0.101 0.106 0.187m = 3 0 0 0 0 0 0 0 0 0.106 0.109 0.137 0.378m = 4 0 0 0 0 0 0 0 0 0.128 0.159 0.283 0.712m = 5 0 0 0 0 0 0 0 0 0.147 0.249 0.401 0.796m = 6 0 0 0 0 0 0 0 0 0.150 0.383 0.552 0.916Thailandm = 2 0 0 0 0 0 0 0 0 0.031 0.135 0.575 0.980m = 3 0 0 0 0 0 0 0 0 0.131 0.350 0.908 0.599m = 4 0 0 0 0 0 0 0 0 0.319 0.596 0.981 0.603m = 5 0 0 0 0 0 0 0 0 0.418 0.664 0.982 0.710m = 6 0 0 0 0 0 0 0 0 0.251 0.495 0.751 0.952

Note: Table reports p-values for BDS (Brock et al. 1996) tests for pure randomness in returns(log changes in US dollar values of equity price indexes), residuals from VAR(1) ltering of the

returns series including contemporaneous values of the 3 month US T-bill, and thestandardized structural residuals from the SGARCH model tted to the VAR residuals. Theparameter " sets the benchmark for comparing distances between consecutive pairs of points

in the test sample and the embedding dimension, m, sets the number of pairs in eachcomparison set. See Brock et al. (1996) for details.

38

Table 4:Parameter Estimation Results: Tranquil Periods

TO market i (yi)Hong Kong Indonesia Korea Thailand(HK) (IN) (KO) (TH)

FROM market j; (yj)Hong Kong bi;HK 0.103 -0.125 0.263

(0.003) (0.050) (0.000)Indonesia bi;IN 0.086 0.148 0.152

(0.001) (0.006) (0.000)Korea bi;KO 0.296 0.009 0.098

(0.000) (0.812) (0.031)Thailand bi;TH 0.032 0.034 0.024

(0.533) (0.430) (0.642)

Note: Parameter estimates for the model B�Yt= ut; where (B+BcDt +DtBs)Yt = B�Y with

BcDt +DtBs representing the linkages present in crisis periods. Estimation is by QML overdaily ltered returns to equity market indices, sampling 6 January 1992 to 9 January 2007.

P-values are in brackets.

39

Table 5:Parameter Estimation Results: Hypersensitivity During Crises in market i

TO market i (yi) when Dit = 1Hong Kong Indonesia Korea Thailand(HK) (IN) (KO) (TH)

FROM market j; (yj)Hong Kong bs;i;HK -2.050 -1.981 0.424

(0.191) (0.246) (0.451)Indonesia bs;i;IN 0.814 -0.753 0.238

(0.000) (0.031) (0.168)Korea bs;i;KO -0.751 -0.636 -0.687

(0.013) (0.505) (0.415)Thailand bs;i;TH 0.475 1.346 0.927

(0.234) (0.341) (0.467)

Note: Parameter estimates for the model B�Yt= ut; where (B+BcDt +DtBs)Yt = B�Y with

BcDt +DtBs representing the linkages present in crisis periods. Each period of crisis isidentied using an indicator variable Di;t which is one during the crisis in home country i andzero otherwise. Hypersensitivity (indicated by subscript s) is given by the parameter bs;ij ineach equation, operating when Dit = 1; measuring the additional impact of foreign shocksduring a domestic crisis. The relevance of each instance of hypersensitivity is tested by thesignicance of the parameters bs;ij. Estimation is by QML over daily ltered returns to equity

market indices, sampling 6 January 1992 to 9 January 2007. P-values are in brackets.

40

Table 6:Parameter Estimation Results: Contagion During Crises in market j:

TO market i (yi)Hong Kong Indonesia Korea Thailand(HK) (IN) (KO) (TH)

FROM market j; (yj) when Djt = 1Hong Kong bc;i;HK 0.180 0.665 -0.504

(0.263) (0.003) (0.021)Indonesia bc;i;IN 0.128 0.145 -0.127

(0.266) (0.488) (0.569)Korea bc;i;KO -0.153 0.727 -0.007

(0.276) (0.001) (0.917)Thailand bc;i;TH -0.175 -0.051 -0.092

(0.128) (0.654) (0.229)

Note: Parameter estimates for the model B�Yt= ut; where (B+BcDt +DtBs)Yt = B�Y with

BcDt +DtBs representing the linkages present in crisis periods. Each period of crisis isidentied using an indicator variable Di;t which is one during the crisis in home country i andzero otherwise. Contagion (indicated by subscript c) is modelled as the additional impact onasset markets in home country i during a crisis in foreign country j; given by the parameterbs;ij in each equation, operating when Djt = 1: The relevance of each instance of contagion istested by the signicance of the parameters bc;ij. Estimation is by QML over daily lteredreturns to equity market indices, sampling 6 January 1992 to 9 January 2007. P-values are in

brackets.

41

Table 7:GARCH parameter estimates

Structural Shocksi Hong Kong Indonesia Korea Thailand

Constant i 0.029 0.070 0.079 0.115(0.036) (0.020) (0.002) (0.037)

ARCH �i 0.089 0.181 0.126 0.171(0.000) (0.000) (0.000) (0.003)

GARCH � i 0.897 0.809 0.859 0.797(0.000) (0.000) (0.000) (0.000)

Note: Parameter estimates for the conditional covariance matrix of the structural shocks,Gt = diag[ + � (ut�1 � ut�1)] + �Gt�1;where is a 4� 1 vector of constants, � is a 4� 4 diagonal

matrix of ARCH coe¢ cients and � is a 4� 4 diagonal matrix of GARCH coe¢ cients.Estimation is by QML over daily ltered returns to equity market indices, sampling 6 January

1992 to 9 January 2007. P-values are in brackets.

42

Table 8:Mean Conditional Forecast Error Variance Decomposition (One Step Ahead)

"i Hong Kong Indonesia Korea Thailand portfolio

TranquilHong Kong 80.38 1.10 0.81 5.04 15.56

[61.89 - 95.19] [0.12-3.42] [0.20-2.39] [1.56-11.82] [4.81-38.40]Indonesia 3.06 98.74 1.99 5.33 30.88

[0.44-9.16] 96.30-99.83] [0.39-5.53] [0.91-15.27] [10.79-63.63]Korea 16.59 0.16 97.21 4.76 39.47

[4.06-33.57] [0.03-0.42] [93.06-99.23] [1.20-11.59] [16.11-64.30]Thailand 0.00 0.00 0.00 84.87 14.09

[0.00-0.00] [0.00-0.00] [0.00-0.00] [69.44-94.98] [4.32-29.80]

HypersensitivityHong Kong 31.26 1.32 1.83 6.25 21.29

[7.71-65.00] [0.15-64.09] [0.42-5.63] [1.85-14.93] [4.72-48.28]Indonesia 55.99 98.23 32.44 20.56 60.36

[24.38-86.43] [95.10-99.74] [11.17-65.11] [4.72-50.79] [29.49-88.91]Korea 12.75 0.45 65.73 0.27 4.06

[3.60-26.13] [0.08-1.17] [33.99-87.28] [0.07-0.66] [1.05-9.22]Thailand 0.00 0.00 0.00 72.91 14.29

[0.00-0.00] [0.00-0.00] [0.00-0.00] [44.37-91.19] [3.50-31.46]

ContagionHong Kong 70.91 11.75 15.29 1.19 22.01

[48.07-91.80] [02.79-32.02] [4.75-37.83] [0.35-12.88] [7.80-50.37]Indonesia 3.28 41.92 3.23 4.06 16.34

[0.51-9.65] [17.21-75.20] [0.68-9.05] [0.67-11.67] [4.44-40.63]Korea 25.81 46.33 81.49 5.56 57.17

[47.22-47.98] [19.60-71.35] [58.57-93.48] [1.35-13.57] [289.63-79.18]Thailand 0.00 0.00 0.00 89.19 4.47

[0.00-0.00] [0.00-0.00] [0.00-0.00] [76.38-96.88] [1.30-9.73]

Note: Conditional one-step ahead error variance decompositions, computed for individualassets and an equally-weighted portfolio of market indices. Rows show the mean of empiricalhistogram of the conditional variance decompositions, conditioning on each standard deviation

gii;t in the sample, and gures in square brackets are the 5th and 95th quantiles.